SOLUTION: Momence, Illinois, is 12 miles upstream on the same side of the river from Kankakee, Illinois, on the Kankakee River. A motorboat that can travel 8 mph in still water leaves Moment

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Question 1153860: Momence, Illinois, is 12 miles upstream on the same side of the river from Kankakee, Illinois, on the Kankakee River. A motorboat that can travel 8 mph in still water leaves Moment and travels downstream toward Kankakee. At the same time, another boat that can travel 10 mph leaves Kankakee and travels upstream toward Momence. Each boat completes the trip in the same amount of time. Find the rate of the current.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
                   SPEED            TIME           DIST.

M to K            8+c               12/(8+c)       12

K to M            10-c              12/(10-c)      12

                             12%2F%288%2Bc%29=12%2F%2810-c%29

Solve the equation for c.



If you have more examples just like this, then using G for the downstream boat and L for the upstream boat, G%3EL, D for distance each way, c for unknown speed of the river, then:
           SPEED      TIME     DIST.
MtoK       L+c        D/(L+c)   D
KtoM       G-c        D/(G-c)   D

D%2F%28G-c%29=D%2F%28L%2Bc%29
-
1%2F%28G-c%29=1%2F%28L%2Bc%29
G-c=L%2Bc
G-L=2c
highlight_green%28c=%28G-L%29%2F2%29